relating the integral of the rotation of a vector field over a surface Σ in Euclidean 3 space to the integral of the vector field over its boundary, is a special case of the general Stokes theorem (with n = 2) once we identify a vector field with a 1 form using the metric on Euclidean 3 space.
The first known statement of the theorem is by William Thomson (Lord Kelvin) and appears in his letter to Stokes.